The Indian army said Pakistani forces on Monday attacked one of their patrol units along the de facto border.
It added that mutilating the bodies was an "unsoldierly act".
Pakistan has denied the allegation, saying its army "was a highly professional force" that would "never disrespect a soldier".
India's Defence Minister Arun Jaitley said the incident was "reprehensible and inhuman", adding that such acts "do not take place even during war".
"Such acts are unheard of even during wars and definitely never in peace time," he said in a statement broadcast on Indian television.
"The entire country has full faith in the army that they will give the appropriate response."
Claimed by both countries, Kashmir has been a flashpoint for more than 60 years.